Method and apparatus for supporting estimation of link acquisition time in satellite-based networks

ABSTRACT

The present invention provides a method and apparatus for supporting estimation of inter-satellite link acquisition times in a satellite constellation. The method includes computing or generating an indication of a statistical model based on observations for prior link acquisition times. The method further includes communicating an indication such as a statistical model for link acquisition times or related parameters through a communication network, or a combination thereof. The indication may be communicated using one or more transmission techniques or protocols, such as flooding, a link state protocol or gossip protocol. Based on the disseminated indication, future link acquisition times can be predicted by satellites in the satellite constellation. Embodiments of the invention use a statistical-based computation approach, such as regression modelling or random variable modelling, to estimate link acquisition times or associated estimation parameters. The estimates or associated estimation parameters may then be disseminated through the constellation.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is the first application filed for the present invention.

FIELD OF THE INVENTION

The present invention pertains to satellite-based networks, such asoptical satellite mesh networks, and in particular to a method andapparatus for estimating acquisition times for satellite links in suchnetworks, and for disseminating related information through the network.

BACKGROUND

Low earth orbit (LEO) satellite constellations are being developed toprovide, among other things, Internet routing services. A LEOconstellation can be thought of as a group of satellites distributed inspace so that they can be organized into a mesh network. Free spaceoptical (i.e. laser) links can be used to provide inter-satellite links(ISLs). A LEO constellation with both ISLs and terrestrial links can beused to provide high-bandwidth network. Other types of ISLs, such asradio frequency (RF) or microwave-based links are also possible. One ofthe technical issues with ISLs in polar orbit LEO constellations is thatinter-satellite links periodically experience signal loss due to therelative motion of the satellites in the constellation. This occurs forexample when satellite orbits cross (e.g. at or near the poles), and theeast-west links are swapped. Other examples occur at the seam of a polarorbit constellation and in the east-west links for constellations withorbits tilted away from the poles (e.g. Walker Delta constellations).The seam refers for example to a boundary such that, on one side of theboundary are satellites in one of two counter-rotating hemispheres orspheres, and on the other side of the boundary are satellites in theother one of the two counter-rotating hemispheres or spheres.Communication links between satellites in different ones of the twocounter-rotating hemispheres or spheres cross the seam.

Reacquiring an inter-satellite link after a loss of connectivity can bea time-consuming process. In the current literature, current opticallink acquisition time (e.g. spatial acquisition time) is estimated torange from 10 to 60 seconds. Most of this time is due to the need forspatial acquisition operations, in which communication lasers onadjacent satellites are aimed correctly at respective receivers.

Because link acquisition times are relatively long in the context of thelife of the link in many situations, link outages are impactful tonetwork operations. Therefore, there is a need to for a method andapparatus for estimating link acquisition times and disseminatingrelated information through the network, so that the impact of linkoutages can be mitigated.

This background information is provided to reveal information believedby the applicant to be of possible relevance to the present invention.No admission is necessarily intended, nor should be construed, that anyof the preceding information constitutes prior art against the presentinvention.

SUMMARY

An object of embodiments of the present invention is to provide a methodand apparatus for supporting estimation of inter-satellite linkacquisition times in a satellite constellation. The method and apparatusis provided for estimating satellite communication link acquisitiontimes, for disseminating information such as link acquisition times orrelated parameters through a communication network, or a combinationthereof. Embodiments of the invention use a statistical-basedcomputation approach to estimate link acquisition times or associatedestimation parameters. The estimates or associated estimation parametersmay then be disseminated through the constellation. The estimation ofthe inter-satellite link acquisition times can be performed locally,remotely or a combination thereof.

In accordance with embodiments of the present invention, there isprovided a method for supporting the estimation of inter-satellite linkacquisition times in a satellite constellation. The method may beperformed by a suitable device, such as a computing and communicationdevice of a first satellite of the satellite constellation. The methodincludes determining an indication of a statistical model. Theindication may be determined based on observations involving priorinter-satellite link acquisitions by the first satellite. Thestatistical model is configured to estimate future inter-satellite linkacquisition times involving the first satellite. The method furtherincludes communicating the indication of the statistical model towardone or more other satellites in the satellite constellation. Theindication may then be used by the one or more other satellites or oneor more other network entities to operate the statistical model forestimating the future inter-satellite link acquisition times involvingthe first satellite.

In accordance with embodiments of the present invention, there isprovided an apparatus of a satellite of a satellite constellation forsupporting estimation of inter-satellite link acquisition times in thesatellite constellation. The apparatus includes suitable computingelectronics such as a processor and a memory storing machine executableinstructions. The apparatus is configured, for example by configurationof the instructions, to compute an indication of a statistical model andto communicate the indication of the statistical model. The computing isbased on observations involving prior inter-satellite link acquisitionsby the satellite. The statistical model is configured to estimate futureinter-satellite link acquisition times involving the satellite. Theindication of the statistical model is communicated toward one or moreother satellites in the satellite constellation. The indication may thenbe used by the one or more other satellites or one or more other networkentities to operate the statistical model for estimating the futureinter-satellite link acquisition times involving the satellite.

In accordance with embodiments of the present invention, there isprovided an apparatus for supporting estimation of inter-satellite linkacquisition times in the satellite constellation. The apparatus includessuitable computing electronics such as a processor and a memory storingmachine executable instructions. The apparatus is configured, forexample by configuration of the instructions, to receive an indicationof a statistical model and to operate the statistical model. Thestatistical model is computed based on observations involving priorinter-satellite link acquisitions by a remote satellite. The statisticalmodel is configured to estimate future inter-satellite link acquisitiontimes involving the remote satellite. Operating the statistical model isperformed, using the indication, for estimating said futureinter-satellite link acquisition times involving the remote satellite.

Embodiments have been described above in conjunctions with aspects ofthe present invention upon which they can be implemented. Those skilledin the art will appreciate that embodiments may be implemented inconjunction with the aspect with which they are described, but may alsobe implemented with other embodiments of that aspect. When embodimentsare mutually exclusive, or are otherwise incompatible with each other,it will be apparent to those skilled in the art. Some embodiments may bedescribed in relation to one aspect, but may also be applicable to otheraspects, as will be apparent to those of skill in the art.

BRIEF DESCRIPTION OF THE FIGURES

Further features and advantages of the present invention will becomeapparent from the following detailed description, taken in combinationwith the appended drawings, in which:

FIG. 1 illustrates an example of a satellite network integrated with aterrestrial network.

FIG. 2 illustrates unpredictability of link acquisition times in thesatellite network and its potential impact to network operations.

FIG. 3 illustrates, in a flow diagram, a method for supportingestimation of inter-satellite link acquisition times in a satelliteconstellation, in accordance with embodiments of the present invention.

FIG. 4 illustrates, in a block diagram, a portion of a satelliteconstellation with a plurality of satellites connected together in amesh network, in accordance with embodiments of the present invention.

FIG. 5 illustrates, in a schematic diagram, an electronic device inaccordance with embodiments of the present invention.

It will be noted that throughout the appended drawings, like featuresare identified by like reference numerals.

DETAILED DESCRIPTION

As used herein, the term “about” should be read as including variationfrom the nominal value, for example, a +/−10% variation from the nominalvalue. It is to be understood that such a variation is always includedin a given value provided herein, whether or not it is specificallyreferred to.

FIG. 1 illustrates an example of a satellite network integrated withterrestrial network. Referring to FIG. 1, there is provided a satellitenetwork 100 integrated with terrestrial network. The satellite network100 includes LEO satellites 110 and 120 in a satellite constellation.The LEO satellites 110 and 120 may be placed into different orbits. TheLEO satellites 110 and 120 can be interconnected by optical crosslinks.The LEO satellites 110 and 120 are connected to terrestrial userterminals. Optical fiber 135 and wireless networks 130 interconnect withthe satellites via gateways 140 forming a global heterogeneous network.Data networks based on such LEO constellation topologies illustrated inthe figure can provide data networking services, especially in areas ofpoor or congested terrestrial infrastructure deployment.

Low earth orbit (LEO) satellite constellations are capable of providing,among other things, internet routing services. To provide internetrouting services, link state routing is the dominantly used as theinterior gateway routing method in satellite network operations as thelink state routing takes condition of network link into considerationwhen performing routing computation.

Satellite links can be occasionally or periodically interrupted due forexample to operational problems or satellite position. Re-acquisition ofinterrupted links is then required. Because links cannot be used duringtheir acquisition, it is useful for other satellites in a constellationor network to be informed of the time that link acquisition is completedor expected to be completed. This assists such satellites in correctlymaking routing decisions involving the link subject to re-acquisition.

Existing approaches such as U.S. Patent Application Publication No.2003/0137930 provide methods and apparatuses for routing information insatellite (communication) networks. Some existing approaches usessatellite ephemeris data to predict link state changes in the satellitemesh or constellation in which the LEO satellites are organized. Thesatellite ephemeris data may include information relating to thesatellite trajectory, such as the satellite locations (or velocities)over time, and information relating to state of the satellites.

In existing approaches, it is proposed to use almanac data for thenetwork nodes (e.g. satellites) which are not adjacent to (e.g. areremotely situated from) the satellite link that changes its state, inorder to predict the satellite link state changes. The almanac data mayinclude coarse orbit and status information for each satellite in thesatellite constellation. The network nodes adjacent to the satellitelink changing its state, on the other hand, suppress updating the linkstate thereof.

In embodiments, almanac data may refer to information regardingoperational information for satellites in a constellation. Theoperational information may include orbital (e.g. position and velocity)information, satellite state information, coarse communication linkcapabilities information, etc.

This approach is proposed with the intention to avoid constant floods oflink state updates where the link state changes are predictable.Regarding the link state changes, prior art do not take into account thestochastic nature of satellite link acquisition as they consider thelink state updates to occur due to known movement of satellites.

However, link state changes cannot always be predicted easily. This isbecause link acquisition times can vary over relatively wide range andtherefore are unpredictable, as is illustrated in FIG. 2. Further,satellite emulators generally model link acquisition times as a randomvariable. This makes harder to predict when the link will be up. FIG. 2illustrates unpredictability of link acquisition times in the satellitenetwork and its potential impact to network operations. In particular,FIG. 2 illustrates a time 205 at which a link disconnects, and a time210 at which a new link acquisition operation starts. Although the worstcase link acquisition time 220 may be known and predictable, the actuallink acquisition time 215 is not necessarily predictable, other thanknowing that it is before the worst case time 220. In the time 225between the actual link acquisition time 215 and the worst-case time220, the link is ready for use but is not usable, because the network isconfigured to wait until the worst case time 220 before using the link.

However, simply using worst link acquisition time is not a desire\ableoption, as it will reduce network throughput and utilization. ReferringFIG. 2, use of the worst-case link acquisition time can causeunnecessary delay throughout the network (e.g. link is ready but notusable by the network), especially when the link is reacquired earlierthan the worst link acquisition time. On the other hand, if the linkreacquisition is prematurely declared, the premature declaration mayresult in routing black holes, packet loss and its follow on effects.

According to various embodiments, computing equipment associated with(e.g. on board) a satellite can be used to record a history of linkacquisition times (e.g. prior link acquisition times), potentially alongwith related information. The related information can include, forexample, absolute satellite position, relative satellite position withrespect to other satellites, time, distance, location and/or velocity ofthe satellite, distance, location and/or velocity of a satellite at afar end of the link, etc. In some embodiments, computing equipmentassociated with a satellite may be located remotely from the satellitewhile communicatively connected thereto.

The history (e.g. prior link acquisition times) can be used to estimatefuture link acquisition times. In some cases the estimates can besubstantially independent of other observations. For example, if linkacquisition times are historically approximately Gaussian distributedwith a mean of μ and a variance σ², then the link acquisition time canbe estimated according to such a distribution. For example, the linkacquisition time can be estimated to be less than or equal to μ+2σ² withprobability of about 0.9545 according to standard statistical analysis.In some cases, the estimates can depend on other observations. Forexample, the history can be processed to infer that the link acquisitiontimes are distributed according to a certain probability distributionwhich has parameters that are a function of one or more otherobservables such as satellite position (e.g. absolute position of thesatellite or relative position of the satellite with respect to othersatellite) and inter-satellite distance. Accordingly, the linkacquisition time can be estimated according to such a distribution,taking into account current values for such observables.

More generally, the history can be used to determine an indication of amodel that can be used to estimate future link acquisition timesinvolving a given satellite. The indication can be the model itself orparameters of the model. The model generally refers to a statisticalmodel, which can involve one or more approaches such as regression,statistical filtering, maximum likelihood estimation, maximum aposteriori estimation, expectation maximization, hidden Markov models,or other approaches. The parameters can be parameters (e.g. mean andvariance) of a statistical distribution, or state transitionprobabilities in a hidden Markov model, parameters describing randomvariable behaviour or correlations between variables, etc.

In some embodiments, each satellite will need to have a routing enginethat makes routing decisions based on state of remote links (e.g. linksnot originating or terminating at the satellite in question) in thesatellite network system. The state of a remote link is closely relatedto whether the remote link's link acquisition process has completed.Embodiments of the present invention provide for methods and apparatusfor estimating the probability that a remote link has been re-acquired(e.g. completion of link acquisition) at a specific time and isoperational after a link outage. This estimate can be used in makinginformed routing decisions.

According to various embodiments, satellite routing engines estimatelink acquisition times in accordance with observation and computation.Related information (e.g. parameters of a statistical model) is thendistributed through the constellation. Other satellites, upon receipt ofthe information, use this information to predict remote link acquisitiontimes more accurately. It is noted that satellites do not necessarilyneed to predict local link acquisition times because these are observeddirectly. Those skilled in the art will appreciate that colloquialreference to a satellite instead of satellite routing engine may beused.

FIG. 3 illustrates a method for supporting estimation of inter-satellitelink acquisition times in a satellite constellation, in accordance withembodiments of the present invention. The method illustrated in FIG. 3may be performed by one or more computing and communication devices ofsatellites in the satellite constellation. In some embodiments, thecomputing and communication devices may be integrated with thus part ofthe satellites. In some embodiments, the computing and communicationdevices may be separate from the satellites but communicativelyconnected thereto. Referring to FIG. 3, embodiments of the presentinvention involve a first satellite or other satellites learning 310information indicative of link acquisition times based on observations.In at least one embodiment, a satellite, or the routing engine of thesatellite, learns about link acquisitions associated with the links thatoriginate or terminate with the same satellite. The link acquisitioninformation can be carried in the form of a statistical model orparameters thereof. Embodiments further involve the first satellite orother satellites communicating 320 the information indicative of thelink acquisition times (i.e. the indication of the statistical model forlink acquisition times) to the first satellite or other satellites inthe satellite constellation. Embodiments further involve, by the firstsatellite or other satellites, predicting 330 link acquisition times,for example based on received information indicative of the linkacquisition times.

The observation may be performed by the first satellite or other networkentities (e.g. network node, other satellites) remotely situated fromthe first satellite. If the observation is made by network entitiesother than the first satellite, then network entities are operatively orcommunicatively connected to the first satellite. In such cases,observation results acquired by the network entities other than thefirst satellite may be transmitted to the first satellite. Theobservation results may include link acquisition times involving thefirst satellite.

The information indicative of the link acquisition times can includelink acquisition time estimates. The information indicative of the linkacquisition times can include a statistical model or parameters thereoffor use in estimating or predicting link acquisition times. Theparameters can be statistical parameters (e.g. mean, variance,distribution type), model parameters (e.g. structure of a model used toestimate link acquisition times), etc.

Learning 310 the link acquisition information based on observations caninclude receiving or collecting the observations and processing theobservations. The processing may also include computing an indication ofa statistical model (for link acquisition times) based on theobservations involving prior inter-satellite link acquisitions by thefirst satellite. The observation (or observation result) may includedistance between satellites, absolute and relative satellite velocities,strength of the laser transmitter and others. In some embodiments theinformation may be specific to specific pairings of satellites. Invarious embodiments, the processing may be performed by the firstsatellite. In some embodiments, the processing may be performed by othernetwork entities (e.g. one or more of other satellites, network entitiesof a terrestrial network) remotely situated from the first satellite. Insuch cases, observation results acquired by the first satellite may betransmitted to one or more network entities other than the firstsatellite so that the one or more network entities can perform theprocessing with the observation result received from the firstsatellite. The indication of the statistical model can include thestatistical model itself or parameters of the statistical model. Theprocessing can be based on statistical techniques, such as regressionmodelling, random variable modelling or other computational methods forestimating relationships among variables. For example, in someembodiments, regression modeling can be used to generate the statisticalmodel for link acquisition times based on independent variables. Theindependent variables can indicate, for example, some or all of:distance between satellites; relative satellite velocities; and thestrength of the laser transmitter.

In some embodiments, the link acquisition times can be treated as randomvariables which are modelled (e.g. using statistical modelling). Inorder to model the random variables (e.g. link acquisition times),statistical functions such as probability density functions can be used.Parameters of the statistical function (e.g. probability densityfunction parameters) may be estimated using statistical inferencetechniques, such as maximum likelihood estimation, maximum a posterioriestimation, expectation maximization, hidden Markov models, or othertechniques. For example, using maximum likelihood estimator, the valuesof parameters of the probability density function will be determinedsuch that the values of the parameters maximize the output of thelikelihood (or probability) function (i.e. parameter values that makethe data most likely). The likelihood function can be expressed asL=p(X|Θ), where X represents sampled data set of link acquisition times,and Θ represents the parameters of the probability density function. Putanother way, using maximum likelihood estimator, the probability densityfunction parameters will be chosen such that the likelihood (i.e. L) oflink acquisition times (i.e. X) is maximum. According to embodiments,the statistical model can specify a probability distribution for suchrandom variables, such as truncated normal (Gaussian) distribution(truncated on the left), exponential distribution or other applicableprobability distribution, with certain known or unknown parameters (e.g.distribution type, mean and variance).

Communicating 320 the information indicative of the link acquisitiontimes (i.e. the indication of the statistical model for link acquisitiontimes) can involve transmitting the statistical model for linkacquisition times or parameters of such a statistical model. In variousembodiments, the communicating 320 may be performed by the firstsatellite. In some embodiments, the communicating 320 may be performedby other network entities (e.g. one or more of other satellites, networkentities of a terrestrial network) remotely situated from the firstsatellite. For instance, communicating 320 may be performed by networkentities other than the first satellite when these network entitiesprocessed the observation results transmitted from the first satellite.In such case, the observation results may be processed as describedabove (e.g. processed the observation results based on statisticaltechniques, such as regression modelling, random variable modelling orother computational methods for estimating relationships amongvariables). In some embodiments, communicating may be the transmissionof link acquisition information by the first satellite. Thistransmission may be directed to one or more neighboring satellites usinginter-satellite links. In some embodiments, this transmission may bedone using a ground link to a terrestrial node that can aggregate thisinformation from a plurality of different satellites and re-distributethis information in any of a number of forms including as part of as analmanac.

According to embodiments, the indication of the statistical model can becommunicated through one or more protocols. These can include flooding,link state protocols or gossiping protocols. In some embodiments, theindication may be communicated to other network nodes (e.g. the firstsatellite, other satellites or other network entities of a terrestrialnetwork) using a flooding technique. In some embodiments, the floodingtechnique may be integrated with a link state protocol. In someembodiments, the indication may be communicated using gossip protocols.The gossip protocols may be similar to flooding technique but withreduced messaging. In some embodiments, the indication may becommunicated to other network nodes (e.g. the first satellite, othersatellites or other network entities of a terrestrial network) usingentities (e.g. ground station) of the terrestrial network.

Once the indications of the statistical model for link acquisition timesare communicated, a future link acquisition time involving the firstsatellite is predicted 330, for example based on received informationindicative of the link acquisition times (i.e. the indication of thestatistical model for link acquisition times). According to embodiments,the indication of the statistical model for link acquisition times maybe used by the satellites (e.g. first satellite or other satellites) orother network entities (e.g. network entities of a terrestrial network)to operate the statistical model for estimating the futureinter-satellite link acquisition times involving the first satellite. Assuch, the estimation of the future inter-satellite link acquisitiontimes can be performed locally, remotely or a combination thereof. Theremote estimation of the future acquisition times may include theestimation at least partly performed by entities of the terrestrialnetwork (e.g. entities on the ground). Some embodiments may predict 330the probability that the link acquisition is complete at a specific timeusing the indication of the statistical model. In various embodiments,predicting 330 may be performed by satellites other than the firstsatellite mentioned above in the satellite constellation. However, insome embodiments, predicting 330 can be also performed by the firstsatellite.

According to embodiments, the nominal link acquisition time may bedetermined based on the indication of the statistical model communicatedin step 320 above. The indication can include the statistical modelitself or parameters of the statistical model. The values of theparameters of the statistical model may be provided or determined in thecourse of performing step 310 above.

In one case, a satellite remotely situated from the satellite providingthe indication of the statistical model may predict the future linkacquisition time involving the first satellite using the indication ofthe statistical model such as a regression model. The indication mayinclude the statistical model itself or parameters thereof. The remotesatellite may determine a nominal link acquisition time using almanacdata (e.g. coarse orbit and status information for each satellite (anysatellites) in the satellite constellation). Then, the nominal linkacquisition time may be adjusted using the indication of the statisticalmodel.

In another case, a satellite remotely situated from the satelliteproviding the indication of the statistical model (e.g. the firstsatellite) may predict the probability that the link acquisition iscomplete using the indication of the statistical model such as randomvariable model. The indication may include the statistical model itselfor parameters thereof. The remote satellite may determine a nominal linkacquisition time based on the probability density function. For example,the nominal link acquisition time may be determined such that theprobability for completion of an inter-satellite link acquisition (i.e.such that the link is ready to be used) is 0.9 (or some other suitablyhigh value). The parameters of the probability density function may beestimated at step 310 above, using statistical inference techniques,such as maximum likelihood estimation, maximum a posteriori estimation,expectation maximization or hidden Markov models, or other techniques.

In some embodiments, the determined nominal link acquisition time may becommunicated to the rest of the satellite network (e.g. other satellitesin the satellite constellation, entities communicatively or operativelyconnected to satellites in the satellite constellation) as required.

It should be understood that a node remote to the first satellite,receive link acquisition information from the first satellite and aplurality of other satellites in repeated instances of step 330. When aroute from the node is determined, the link acquisition time for aplurality of different links in the network can be used to determine alikelihood that a link will be available, and this information can beused in a path selection process.

FIG. 4 is a block diagram illustrating a portion of a satelliteconstellation 400 with a plurality of satellites connected together in arectangular mesh, in accordance with embodiments of the presentinvention. Referring to FIG. 4, on the left side of the seam 440 arefive satellites, denoted by general reference numbers 410 and 420, andon the right side of the seam 440 are two satellites 430. The seam 440refers to a boundary dividing the satellites into two groups such thatthe satellites 410 and 420 are in one of two counter-rotatinghemispheres and the satellites 430 are in the other one of twocounter-rotating hemispheres. The satellites in each hemisphere arecounter-rotating in opposite directions. The satellites 410, 420 and 430may be operatively or communicatively connected to each other asillustrated in FIG. 4. Communication links between satellites indifferent ones of the two counter-rotating hemispheres (i.e. satellites410, 420 vs. satellites 430) can cross the seam 440. Satellites canalternatively be arranged in other ways, for example in two or morecounter-rotating spheres.

The satellite 410 may include a router 411, almanac function 412, linkstate database 413, and observation database 414. The router 411 may bea network interface that receives data from and transmits data to othersatellites. The almanac function 412 may collect or provide almanac datasuch as coarse orbit and status information for each satellite in thesatellite constellation. The link state database 413 may be operativelyor communicatively connected to the router 411. The link state database413 may hold information describing the satellite network topology,including current status of links in the network. The information storedin the link state database 413 may be in great detail such that theshortest path to a network node can be computed based on the most recentinformation available from the link state database 413. The observationdatabase 414 may be part of the link state database 413 of the router411 as shown in the figure. In some embodiments, the observationdatabase 414 is not part of the link state database 413 but a separatedatabase. While differently labelled, the satellites 420 and thesatellites 430 have same or similar components as the satellite 410.

According to embodiments, the satellite 410 may observe inter-satellitelink acquisitions and measure the link acquisition times as desired. Themeasured link acquisition times may be stored in the observationdatabase 414. The link acquisition times saved in the observationdatabase 414 may be retrieved to compute an indication of a statisticalmodel (e.g. regression model). The statistical model may be configuredto estimate future inter-satellite link acquisition times involving thesatellite 410.

When the link acquisition times are retrieved from the observationdatabase 414, the satellite 410 may compute or generate indication of astatistical model for link acquisition times. The indication of thestatistical model can include a statistical model or parameters thereoffor use in estimating or predicting link acquisition times. Theparameters can include statistical parameters, such as mean linkacquisition time, variance, distribution type, or more generallyparameters of a probability distribution for a random variablerepresenting a quantity such as but not limited to the link acquisitiontime. The parameters can include model parameters, such as the structureof a model used to estimate link acquisition times. Model parameters canindicate one or more variables, such as random variables to be predictedor (partially or fully) observable quantities. Observable quantities caninclude satellite positions, velocities, times, distances, laserstrengths, signal strengths, etc. Model parameters can indicate causalor statistical relationships between such variables. For example, modelparameters can indicate a numerical relationship between linkacquisition time and observable quantities such as inter-satellitedistances, satellite locations, velocities, and signal strengths. Thenumerical relationship can be represented in the form of a mathematicalmodel such as a Bayesian network, a hidden Markov model, a stochasticequation or differential equation, etc.

According to embodiments, the link acquisition times may be modeledusing one or more statistical techniques, such as regression modelling,random variable modelling and other computational methods. In someembodiments, the link acquisition times may be modeled as a function ofthe relative velocity of two satellites.

In some embodiments, parameters of the statistical model for linkacquisition times may be computed using statistical inferencetechniques, such as maximum likelihood estimation, maximum a posterioriestimation, expectation maximization, hidden Markov models, or othertechniques. For example, using maximum likelihood estimator, the valuesof parameters of the statistical model for link acquisition times willbe determined such that the values of the parameters maximize the outputof the likelihood (or probability) function (i.e. parameter values thatmake the data most likely). The likelihood function can be expressed asL=p(X|Θ), where X represents sampled data set of link acquisition times,and Θ represents the parameters of the statistical model. Put anotherway, using maximum likelihood estimator, the parameters of thestatistical model will be chosen such that the likelihood (i.e. L) oflink acquisition times (i.e. X) is maximum.

When the satellite 410 completes computing or generating the indicationof the statistical model (e.g. regression model, random variable model)for the link acquisition time, the satellite 410 may communicate theindication to other satellites (e.g. satellites 420 and 430) in thesatellite constellation. Again, the indication may include modelparameters, for example. One or more routing techniques or transmissionprotocols may be used when forwarding the statistical model to thesatellites 420 and 430. Potential routing techniques or transmissionprotocols include flooding, a link state protocol and gossip protocol.In some embodiments, the flooding technique may be integrated with alink state protocol. In some embodiments, the statistical model may becommunicated or disseminated to other satellites (e.g. satellites 420and 430) as part of link state protocol data unit (PDU) message.

When the satellites 420 and 430 receive the indications of thestatistical model for link acquisition times, these satellites mayrebuild and execute the statistical model using the received indicationsin order to estimate when the links involving the satellite 410 willcompute their link acquisition phase. For that, the satellites 420 and430 may predict future link acquisition times for the links involvingthe satellite 410. In some embodiments, the satellites 420 and 430 maypredict the probability that the link acquisition involving thesatellite 410 is complete at a specific time using the indication of thestatistical model.

According to embodiments, the satellites 420 and 430 may use almanacdata (e.g. coarse orbit and status information for each satellite in thesatellite constellation) provided by their almanac function (i.e.component equating to the almanac function 412) to determine the nominallink acquisition time. The nominal link acquisition time may be adjustedusing the indication of the statistical model to acquire the future linkacquisition time involving the satellite 410.

When future link acquisition time or the probability for completion thelink acquisition is estimated, the satellites 410, 420 and 430 may usethese data to update their local link state database (e.g. link statedatabase 413). The satellites 410, 420 and 430 may also trigger newrouting computations based on these data.

FIG. 5 is a schematic diagram of an electronic device 500 that mayperform any or all of operations of the above methods and featuresexplicitly or implicitly described herein, according to differentembodiments of the present invention. For example, a computer equippedwith satellite or network function may be configured as electronicdevice 500.

As shown, the device includes a processor 510, such as a CentralProcessing Unit (CPU) or specialized processors such as a digital signalprocessor (DSP) or other such processor unit, memory 520, non-transitorymass storage 530, I/O interface 540, network interface 550, and atransceiver 560, all of which are communicatively coupled viabi-directional bus 570. According to certain embodiments, any or all ofthe depicted elements may be utilized, or only a subset of the elements.Further, the device 500 may contain multiple instances of certainelements, such as multiple processors, memories, or transceivers. Also,elements of the hardware device may be directly coupled to otherelements without the bi-directional bus. Additionally or alternativelyto a processor and memory, other electronics, such as integratedcircuits, may be employed for performing the required logicaloperations.

The memory 520 may include any type of non-transitory memory such asstatic random access memory (SRAM), dynamic random access memory (DRAM),synchronous DRAM (SDRAM), read-only memory (ROM), any combination ofsuch, or the like. The mass storage element 530 may include any type ofnon-transitory storage device, such as a solid state drive, hard diskdrive, a magnetic disk drive, an optical disk drive, USB drive, or anycomputer program product configured to store data and machine executableprogram code. According to certain embodiments, the memory 520 or massstorage 530 may have recorded thereon statements and instructionsexecutable by the processor 510 for performing any of the aforementionedmethod operations described above.

Embodiments of the present invention provide advantages in operatingsatellite network system. For instance, embodiments allow the satellitenetwork system to avoid using open loop estimates of link acquisitiontime. This can reduce network downtime due to signal loss on satellitenetwork links thereby enhancing network throughput and utilization. Inlight of stochastic nature of satellite link acquisition, without theproposed method and embodiments each satellite may take veryconservative approaches for estimating when a remote inter-satellitelink will be re-acquired or will be available for use.

It will be appreciated that, although specific embodiments of thetechnology have been described herein for purposes of illustration,various modifications may be made without departing from the scope ofthe technology. The specification and drawings are, accordingly, to beregarded simply as an illustration of the invention as defined by theappended claims, and are contemplated to cover any and allmodifications, variations, combinations or equivalents that fall withinthe scope of the present invention. In particular, it is within thescope of the technology to provide a computer program product or programelement, or a program storage or memory device such as a magnetic oroptical wire, tape or disc, or the like, for storing signals readable bya machine, for controlling the operation of a computer according to themethod of the technology and/or to structure some or all of itscomponents in accordance with the system of the technology.

Acts associated with the method described herein can be implemented ascoded instructions in a computer program product. In other words, thecomputer program product is a computer-readable medium upon whichsoftware code is recorded to execute the method when the computerprogram product is loaded into memory and executed on the microprocessorof the wireless communication device.

Acts associated with the method described herein can be implemented ascoded instructions in plural computer program products. For example, afirst portion of the method may be performed using one computing device,and a second portion of the method may be performed using anothercomputing device, server, or the like. In this case, each computerprogram product is a computer-readable medium upon which software codeis recorded to execute appropriate portions of the method when acomputer program product is loaded into memory and executed on themicroprocessor of a computing device.

Further, each operation of the method may be executed on any computingdevice, such as a personal computer, server, PDA, or the like andpursuant to one or more, or a part of one or more, program elements,modules or objects generated from any programming language, such as C++,Java, or the like. In addition, each operation, or a file or object orthe like implementing each said operation, may be executed by specialpurpose hardware or a circuit module designed for that purpose.

Through the descriptions of the preceding embodiments, the presentinvention may be implemented by using hardware only or by using softwareand a necessary universal hardware platform. Based on suchunderstandings, the technical solution of the present invention may beembodied in the form of a software product. The software product may bestored in a non-volatile or non-transitory storage medium, which can bea compact disk read-only memory (CD-ROM), USB flash disk, or a removablehard disk. The software product includes a number of instructions thatenable a computer device (personal computer, server, or network device)to execute the methods provided in the embodiments of the presentinvention. For example, such an execution may correspond to a simulationof the logical operations as described herein. The software product mayadditionally or alternatively include number of instructions that enablea computer device to execute operations for configuring or programming adigital logic apparatus in accordance with embodiments of the presentinvention.

Although the present invention has been described with reference tospecific features and embodiments thereof, it is evident that variousmodifications and combinations can be made thereto without departingfrom the invention. The specification and drawings are, accordingly, tobe regarded simply as an illustration of the invention as defined by theappended claims, and are contemplated to cover any and allmodifications, variations, combinations or equivalents that fall withinthe scope of the present invention.

We claim:
 1. A method for supporting estimation of inter-satellite linkacquisition times in a satellite constellation, comprising, by acomputing and communication device of a first satellite of the satelliteconstellation: determining an indication of a statistical model based onobservations involving prior inter-satellite link acquisitions by thefirst satellite, the statistical model configured to estimate futureinter-satellite link acquisition times involving the first satellite;and communicating the indication of the statistical model toward one ormore other satellites in the satellite constellation, the indicationused by the one or more other satellites or one or more other networkentities to operate the statistical model for estimating said futureinter-satellite link acquisition times involving the first satellite. 2.The method of claim 1, wherein the communicated indication containsinformation to enable the one or more other satellites to estimate thefuture inter-satellite link acquisition times.
 3. The method of claim 2,wherein the data related to the first satellite or the one or more othersatellites includes almanac data.
 4. The method of claim 1, wherein theone or more other satellites estimate, based on the indication, aprobability for completion of an inter-satellite link acquisitioninvolving the first satellite at a specific time.
 5. The method of claim1, wherein the indication includes the statistical model itself.
 6. Themethod of claim 1, wherein the indication includes one or moreparameters of the statistical model.
 7. The method of claim 6, whereinthe parameters include one or both of: parameters of a probabilitydistribution for a random variable; and causal or statisticalrelationships between random variables, observable quantities, or acombination thereof.
 8. The method of claim 1, wherein the indication ofthe statistical model is communicated using one or more of flooding, alink state protocol, gossip protocol and link stated Protocol Data Unit(PDU) message.
 9. The method of claim 1, wherein the indication iscomputed using one or more statistical inference methods.
 10. The methodof claim 9, wherein the one or more statistical methods includeregression analysis, regression modelling, random variable modelling,maximum likelihood estimation (MLE), maximum a posteriori (MAP),expectation maximization (EM) and hidden Markov model.
 11. The method ofclaim 1, wherein communicating the indication further comprisestransmitting the indication to a node in a terrestrial network.
 12. Themethod of claim 1, wherein the inter-satellite link is between the firstsatellite and a second satellite placed into a same orbit as the firstsatellite, or wherein the inter-satellite link is between the firstsatellite and a second satellite placed into a different orbit from thefirst satellite, or wherein the inter-satellite link is between thefirst satellite and a second satellite communicating with the firstsatellite across a seam.
 13. An apparatus of a satellite of a satelliteconstellation for supporting estimation of inter-satellite linkacquisition times in the satellite constellation, the apparatuscomprising: a processor; and a memory storing machine executableinstructions, the instructions when executed by the processor configurethe apparatus to: compute an indication of a statistical model based onobservations involving prior inter-satellite link acquisitions by thesatellite, the statistical model configured to estimate futureinter-satellite link acquisition times involving the satellite; andcommunicate the indication of the statistical model toward one or moreother satellites in the satellite constellation, the indication used bythe one or more other satellites or one or more other network entitiesto operate the statistical model for estimating said futureinter-satellite link acquisition times involving the satellite.
 14. Theapparatus of claim 13, wherein the indication includes the statisticalmodel itself.
 15. The apparatus of claim 13, wherein the indicationincludes one or more parameters of the statistical model.
 16. Theapparatus of claim 15, wherein the parameters include one or both of:parameters of a probability distribution for a random variable; andcausal or statistical relationships between random variables, observablequantities, or a combination thereof.
 17. The apparatus of claim 13,wherein the indication of the statistical model is communicated usingone or more of flooding, a link state protocol, gossip protocol and linkstated Protocol Data Unit (PDU) message.
 18. The apparatus of claim 13,wherein the indication is computed using one or more statisticalinference methods.
 19. The apparatus of claim 18, wherein the one ormore statistical methods include regression analysis, regressionmodelling, random variable modelling, maximum likelihood estimation(MLE), maximum a posteriori (MAP), expectation maximization (EM) andhidden Markov model.
 20. The apparatus of claim 13, wherein theindication is communicated at least partly through terrestrial network.21. An apparatus for supporting estimation of inter-satellite linkacquisition times in the satellite constellation, the apparatuscomprising: a processor; and a memory storing machine executableinstructions, the instructions when executed by the processor configurethe apparatus to: receive an indication of a statistical model computedbased on observations involving prior inter-satellite link acquisitionsby a remote satellite, the statistical model configured to estimatefuture inter-satellite link acquisition times involving the remotesatellite; and operate the statistical model, using the indication, forestimating said future inter-satellite link acquisition times involvingthe remote satellite.
 22. The apparatus of claim 21, wherein theinstructions when executed by the process further configure theapparatus to: estimate the future inter-satellite link acquisition timesbased on the indication, data related to the satellite, the remotesatellite or other satellites in the satellite constellation, or both.23. The apparatus of claim 22, wherein the data related to thesatellite, the remote satellite or other satellites in the satelliteconstellation includes almanac data.
 24. The apparatus of claim 21,wherein the instructions when executed by the process further configurethe apparatus to: estimate a probability for completion of aninter-satellite link acquisition involving the remote satellite at aspecific time using the indication.